Finite Group Databasebeta

← C31×#8319 #21465078

Subgroups — C31×#8319 #21465078

Order 7936.

954 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×2−1+4C211yesmaximal, characteristic
2C31×#1984C211yesmaximal, characteristic, complemented
3C31×#1477C212yesmaximal, complemented
4C31×#1476C212yesmaximal, complemented
5C31×#1461C211yesmaximal, characteristic, complemented
6C2×C31×2−1+4C411yescharacteristic
7C31×#520—22no—
8C31×#520—22no—
9C31×#520C412yes—
10C31×#519—22no—
11C31×#519C411yescharacteristic
12C4×#41×C31—22no—
13C4×#41×C31—22no—
14C4×#41×C31C2212yes—
15C2×C4×Q8×C31—22no—
16C2×C4×Q8×C31C2211yescharacteristic
17C31×#431C2212yes—
18C2×C31×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C31C2211yescharacteristic
20C31×#336—22no—
21C31×Q8⋊C8—22no—
22C31×Q8⋊C8—22no—
23C31×D4⋊C8—22no—
24C31×D4⋊C8—22no—
25C31×#324—22no—
26C31×2−1+4—24no—
27C31×2−1+4—22no—
28C31×2−1+4C814yescomplemented
29C2×#41×C31—22no—
30C2×#41×C31—22no—
31C2×#41×C31C2×C412yes—
32C22×Q8×C31—22no—
33C22×Q8×C31C2×C411yescharacteristic
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C4×Q8×C31—22no—
37C4×Q8×C31—24no—
38C4×Q8×C31—22no—
39C4×Q8×C31—22no—
40C4×Q8×C31—22no—
41C4×Q8×C31—22no—
42C4×Q8×C31—22no—
43C4×Q8×C31—22no—
44C4×Q8×C31D412yes—
45C4×Q8×C31D412yes—
46C4×D4×C31—22no—
47C4×D4×C31—24no—
48C4×D4×C31—22no—
49C4×D4×C31—22no—
50C4×D4×C31—24no—
51C4×D4×C31—22no—
52C4×D4×C31—22no—
53C4×D4×C31D412yes—
54C4×D4×C31D412yes—
55C31×#117—24no—
56C31×#117—24no—
57C31×#117—22no—
58C31×#117—22no—
59C31×#117—22no—
60C31×#117C2×C412yes—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31C2×C411yescharacteristic
64C2×C4⋊C4×C31D412yes—
65C2×C42×C31—24no—
66C2×C42×C31—22no—
67C2×C42×C31D412yes—
68C2×C42×C31C2311yescharacteristic
69C31×C4⋊C8—22no—
70C31×C4⋊C8—22no—
71C31×C22⋊C8—22no—
72C4×C8×C31—22no—
73C4×C8×C31—22no—
74#41×C31—28no—
75#41×C31—28no—
76#41×C31—28no—
77#41×C31—28no—
78#41×C31—22no—
79#41×C31—22no—
80#41×C31C2×C814yes—
81#41×C31M1614yes—
82C2×Q8×C31—22no—
83C2×Q8×C31—28no—
84C2×Q8×C31—28no—
85C2×Q8×C31—22no—
86C2×Q8×C31—22no—
87C2×Q8×C31C22⋊C412yes—
88C2×Q8×C31C2×C812yes—
89C2×Q8×C31M1612yes—
90C2×D4×C31—22no—
91C2×D4×C31—22no—
92C2×D4×C31C22⋊C412yes—
93C22×C4×C31—24no—
94C22×C4×C31—22no—
95C22×C4×C31—24no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31C22⋊C412yes—
99C22×C4×C31C22⋊C412yes—
100C22×C4×C31C22×C411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103C2×C8×C31—22no—
104C2×C8×C31—41no—
105C2×C8×C31—41no—
106C2×C8×C31—42no—
107C2×C8×C31—42no—
108C2×C8×C31—41no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—24no—
115C4⋊C4×C31—22no—
116C4⋊C4×C31C22⋊C412yes—
117C4⋊C4×C31C22⋊C412yes—
118C22⋊C4×C31—24no—
119C22⋊C4×C31—22no—
120C22⋊C4×C31—22no—
121C22⋊C4×C31—22no—
122C42×C31—24no—
123C42×C31—24no—
124C42×C31—22no—
125C42×C31—22no—
126C42×C31—22no—
127C42×C31—22no—
128C42×C31—22no—
129C42×C31C2×D412yes—
130C42×C31C2×D412yes—
131#8319C3111yesmaximal, characteristic, direct product factor, Sylow
132C23×C31—22no—
133C23×C31C2×C22⋊C411yescharacteristic
134Q8×C31—28no—
135Q8×C31—24no—
136Q8×C31—22no—
137Q8×C31—24no—
138Q8×C31C22⋊C814yes—
139D4×C31—28no—
140D4×C31—24no—
141D4×C31—24no—
142D4×C31—22no—
143D4×C31C22⋊C814yes—
144C2×C4×C31—216no—
145C2×C4×C31—22no—
146C2×C4×C31—22no—
147C2×C4×C31—22no—
148C2×C4×C31—24no—
149C2×C4×C31—24no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—82no—
160C2×C4×C31—84no—
161C2×C4×C31C22⋊C814yes—
162C2×C4×C31C2×C22⋊C412yes—
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12012yes—
165C2×C4×C31#12011yescharacteristic
166C2×C4×C31C22×C811yescharacteristic
167C2×C4×C31C2×M1612yes—
168C2×C4×C31C2×M1611yescharacteristic
169C8×C31—42no—
170C8×C31—82no—
171C8×C31—81no—
172C4×2−1+4C2×C3111yescharacteristic
173#1984C2×C3111yescharacteristic, complemented
174#1477C2×C3112yescomplemented
175#1476C2×C3112yescomplemented
176#1461C2×C3111yescharacteristic, complemented
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—24no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31#37911yescharacteristic
183C22×C31C2×C22⋊C811yescharacteristic
184C22×C31#40711yescharacteristic
185C4×C31—21no—
186C4×C31—22no—
187C4×C31—24no—
188C4×C31—24no—
189C4×C31—42no—
190C4×C31—42no—
191C4×C31—42no—
192C4×C31C2×C22⋊C812yes—
193C4×C31#40712yes—
194C4×C31#45411yescharacteristic
195C4×C31#45611yescharacteristic
196C2×2−1+4C4×C3111yescharacteristic
197#520—22no—
198#520—22no—
199#520C4×C3112yes—
200#519—22no—
201#519C4×C3111yescharacteristic
202C4×#41—22no—
203C4×#41—22no—
204C4×#41C22×C3112yes—
205C2×C4×Q8—22no—
206C2×C4×Q8C22×C3111yescharacteristic
207#431C22×C3112yes—
208C2×C4⋊C8C22×C3111yescharacteristic
209C2×C4×C8C22×C3111yescharacteristic
210#336—22no—
211Q8⋊C8—22no—
212Q8⋊C8—22no—
213D4⋊C8—22no—
214D4⋊C8—22no—
215#324—22no—
216C2×C31—21no—
217C2×C31—21no—
218C2×C31—44no—
219C2×C31#177911yescharacteristic
220C2×C31#179311yescharacteristic
221C2×C31#179411yescharacteristic
2222−1+4—24no—
2232−1+4—22no—
2242−1+4C8×C3114yescomplemented
225C2×#41—22no—
226C2×#41—22no—
227C2×#41C2×C4×C3112yes—
228C22×Q8—22no—
229C22×Q8C2×C4×C3111yescharacteristic
230C22×C8—21no—
231C22×C8—21no—
232C4×Q8—22no—
233C4×Q8—24no—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8D4×C3112yes—
241C4×Q8D4×C3112yes—
242C4×D4—22no—
243C4×D4—24no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—24no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4D4×C3112yes—
250C4×D4D4×C3112yes—
251#117—24no—
252#117—24no—
253#117—22no—
254#117—22no—
255#117—22no—
256#117C2×C4×C3112yes—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4C2×C4×C3111yescharacteristic
260C2×C4⋊C4D4×C3112yes—
261C2×C42—24no—
262C2×C42—22no—
263C2×C42D4×C3112yes—
264C2×C42C23×C3111yescharacteristic
265C4⋊C8—22no—
266C4⋊C8—22no—
267C22⋊C8—22no—
268C4×C8—22no—
269C4×C8—22no—
270C31#831911yescharacteristic, direct product factor, Sylow
271#41—28no—
272#41—28no—
273#41—28no—
274#41—28no—
275#41—22no—
276#41—22no—
277#41C2×C8×C3114yes—
278#41M16×C3114yes—
279C2×Q8—22no—
280C2×Q8—28no—
281C2×Q8—28no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8C22⋊C4×C3112yes—
285C2×Q8C2×C8×C3112yes—
286C2×Q8M16×C3112yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4C22⋊C4×C3112yes—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4C22⋊C4×C3112yes—
296C22×C4C22⋊C4×C3112yes—
297C22×C4C22×C4×C3111yescharacteristic
298C22×C4C2×D4×C3111yescharacteristic
299C22×C4C2×D4×C3111yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—41no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4C22⋊C4×C3112yes—
314C4⋊C4C22⋊C4×C3112yes—
315C22⋊C4—24no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C42—24no—
320C42—24no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42C2×D4×C3112yes—
327C42C2×D4×C3112yes—
328C23—22no—
329C23C2×C22⋊C4×C3111yescharacteristic
330Q8—28no—
331Q8—24no—
332Q8—22no—
333Q8—24no—
334Q8C31×C22⋊C814yes—
335D4—28no—
336D4—24no—
337D4—24no—
338D4—22no—
339D4C31×C22⋊C814yes—
340C2×C4—216no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—82no—
356C2×C4—84no—
357C2×C4C31×C22⋊C814yes—
358C2×C4C2×C22⋊C4×C3112yes—
359C2×C4C31×#12011yescharacteristic
360C2×C4C31×#12012yes—
361C2×C4C31×#12011yescharacteristic
362C2×C4C22×C8×C3111yescharacteristic
363C2×C4C2×M16×C3112yes—
364C2×C4C2×M16×C3111yescharacteristic
365C8—42no—
366C8—82no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—24no—
371C22—42no—
372C22—42no—
373C22C31×#37911yescharacteristic
374C22C2×C31×C22⋊C811yescharacteristic
375C22C31×#40711yescharacteristic
376C4—24no—
377C4—24no—
378C4—21no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—42no—
383C4C2×C31×C22⋊C812yes—
384C4C31×#40712yes—
385C4C31×#45411yescharacteristic
386C4C31×#45611yescharacteristic
387C2—21no—
388C2—21no—
389C2—44no—
390C2C31×#177911yescharacteristic
391C2C31×#179311yescharacteristic
392C2C31×#179411yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#379
prime radicalC2×C31×2−1+4C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#1984C2semidirect
3. C31×#1477C2semidirect
4. C31×#1476C2semidirect
5. C31×#1461C2semidirect
28. C31×2−1+4C8semidirect
131. #8319C31direct (N × H)
173. #1984C2×C31semidirect
174. #1477C2×C31semidirect
175. #1476C2×C31semidirect
176. #1461C2×C31semidirect
224. 2−1+4C8×C31semidirect
270. C31#8319direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×C31×2−1+42
C31×#19842
C31×#14772
C31×#14762
C31×#14612
#831931